Proceedings of the 15th International Heat Transfer Conference, IHTC-15 August 10-15, 2014, Kyoto, Japan

IHTC15-8645

*Corresponding Author: mshah.erc@gmail.com

1

A NEW FLOW PATTERN BASED GENERAL CORRELATION FOR HEAT

TRANSFER DURING CONDENSATION IN HORIZONTAL TUBES

Mirza M. Shah

1*

Engineering Research & Consultation, 10 Dahlia Lane, Redding, CT 06896, USA

ABSTRACT

A flow pattern based general correlation for heat transfer during condensation inside horizontal plain tubes is

presented. It is compared to a data base that contains 89 data sets from 39 studies. It includes 25 fluids

(water, carbon dioxide, DME, halocarbon refrigerants, and hydrocarbon refrigerants), tube diameters from 2 to 49 mm, reduced pressures from 0.0023 to 0.95, flow rates from 13 to 820 kg/m

2s, and all liquid Reynolds

numbers from 1012 to 84827. The 1568 data points are predicted with a mean absolute deviation of 16.7 %,

with flow patterns determined with well-known flow pattern maps. The same data base is also compared to the author’s published correlation which is purely empirical as well as several other general correlations. The

present correlation performs significantly better than other correlations though the author’s published

correlation has slightly lower mean deviation. The results of data analyses are discussed and presented in

graphical and tabular forms.

KEY WORDS: Condensation, Two-phase/Multiphase flow, heat transfer, tubes, correlation

1. INTRODUCTION Prediction of heat transfer during condensation of vapours flowing inside plain tubes is of great importance

as many heat exchangers involve this mode of heat transfer, for example condensers for air conditioning and

refrigeration systems. To ensure optimum design, accurate correlations for prediction of heat transfer are

needed. Many correlations, theoretical and empirical, have been published for heat transfer during condensation inside plain tubes. One of the most widely used has been the author’s correlation [1]. That

correlation is limited to higher flow rates where heat flux has no effect. Shah [2] modified it to extend it to

low flow rates and pressures close to the critical. This correlation has three heat transfer regimes. The boundary between Regime II and III for horizontal tubes for this correlation was not given in [2]; it was

provided in Shah [3]. This correlation was shown to agree with an extremely wide range of data for

horizontal and vertical tubes. It has three heat transfer regimes which are entirely empirical. As noted by many researchers, for example Liebenberg and Meyer [4], correlations that take into consideration flow

patterns are preferable. One benefit of having the correlation in terms of flow patterns is that it opens the

possibility of considering its application to channels of other geometries such as rectangular and triangular

by using flow pattern maps for those geometries. In the present paper, the heat transfer regimes for horizontal round tubes in this correlation have been replaced by flow pattern regimes so as to give it a

physical basis. Thus a flow pattern based general correlation is presented for horizontal tubes. It is shown to

give good agreement with a very wide range of test data from 89 data sets from 39 independent studies. The entire data base is also compared with the Shah [2, 3] correlation as well as a number of other well-known

correlations.

In the following, the development of the correlation is described and its validation with a very wide range of test data is presented. The results of comparison with several other general correlations are also presented.

IHTC15-8645

2

2. THE PUBLISHED SHAH CORRELATION

The flow pattern based correlation presented here is a modification of the published Shah correlation [2, 3].

Hence the published correlation is first given. This correlation has three heat transfer regimes. The

boundaries of these regimes are different for horizontal and vertical tubes. The heat transfer equations are the same for all orientations. This paper is concerned only with horizontal tubes.

2.1 Heat Transfer Equations

The correlation uses the following two heat transfer equations:

)557.00058.0(

95.0 14

8.31

rp

g

lLSI

Zhh

(1)

3/1

2

3

3/1 )(Re32.1

l

lgll

LSNu

gkh

(2)

Eq. (1) is the same as that in the Shah [1] correlation except that it did not have the viscosity ratio factor. Eq. (2)

is the Nusselt equation for laminar film condensation in vertical tubes; the constant has been increased by 20%

as recommended by McAdams [5] on the basis of comparison with test data. This equation can also be expressed in terms of heat flux or temperature difference instead of Reynolds number. This form has been preferred as it is

more convenient for this correlation and often it is also more convenient for design calculations. These equations

are used according to the heat transfer regime as below:

In Regime I,

ITP hh (3)

In Regime II,

NuITP hhh (4)

In Regime III:

NuTP hh (5)

hLS in Eq. (1) is the heat transfer coefficient of the liquid phase flowing alone in the tube. It is calculated by the

following equation:

Dkh llLSLS /PrRe023.0 4.08.0 (6)

Z is the correlating parameter introduced by Shah [1] defined as:

4.08.0)1/1( rpxZ (7)

2.2 Heat Transfer Regimes for Horizontal Tubes

IHTC15-8645

3

The boundaries between were determined by data analysis described in Shah [2, 3]. Regime I occurs when:

62.0)263.0(98.0 ZJ g (8)

Regime III occurs when:

1249.1 )27.2254.1(95.0 ZJ g (9)

If neither of the above conditions are satisfied, it is Regime II.

Jg is the dimensionless vapor velocity defined as:

5.0

)( glg

ggD

xGJ

(10)

3. DEVELOPMENT OF THE FLOW PATTERN BASED CORRELATION

A number of flow pattern maps/correlations have been proposed specifically for condensation inside horizontal

tubes, for example those by Breber et al. [6], Tandon et al. [7], and El Hajal et al. [8]. The El Hajal et al. map has

been validated by using it in comparing the flow pattern based heat transfer correlation of Thome et al. [9] with a

condensation heat transfer database that included many refrigerants and hydrocarbons over a very wide range of parameters. It was therefore the first choice. This correlation has five flow patterns, namely stratified, stratified

wavy, intermittent, annular, and mist. Flow patterns predicted by this correlation were compared with the heat

transfer regimes predicted by the Shah correlation as well as the deviations of the heat transfer coefficients predicted by it. For fluids other than water, it was found that for the vast majority of data:

Heat transfer Regime I corresponded to the intermittent, annular, and mist flow patterns.

Heat transfer Regime II corresponded to stratified-wavy flow pattern.

Heat transfer Regime III corresponded to stratified flow pattern.

For the data of Varma [10] for water, the El Hajal et al. map predicted stratified flow pattern which according to

the results with the other fluids will place it in Regime III and thus Eq. (5) should apply. However, the data

showed agreement with Eq. (4) which corresponds to Regime II for which the data for other fluids indicate the

stratified-wavy flow pattern. The El Hajal et al. map had not been compared to water data. Further, its recommended range of tube diameter is < 21.4 mm while the Varma data are for D = 49 mm, and the minimum

recommended reduced pressure is 0.02 while the Varma data are at a reduced pressure of 0.0023. In view of

these limitations, it was felt that the El Hajal map’s predictions may be incorrect for these data. The Baker [11] map is known to work well with air-water mixtures near atmospheric pressures as well as with many other gas-

liquid mixtures and it was based on data for pipes of diameters from 25 to 100 mm. While it was based on

adiabatic data, it has also been known to work fairly well for non-adiabatic situations. For example, Shah [12]

found it to be in fair agreement with his visual observation on an ammonia evaporator with 25.4 mm diameter tube. It was therefore felt that it may be applicable to the Varma data. The Baker map predicted stratified-wavy

flow pattern and use of Eq. (4) resulted in excellent agreement with the Varma data as seen in Fig. 1.

The Breber et al. map was verified with data that included water but this map does not distinguish between

stratified and stratified-wavy regimes and hence is not useful for the present correlation. The Tandon et al. [7]

map was verified only with refrigerant data. A possible choice for water at higher pressures may be the map of Taitel and Dukler [13] as it was derived analytically. However, that analytical derivation was for adiabatic

condition.

IHTC15-8645

4

0

2000

4000

6000

8000

10000

12000

14000

0.5 0.6 0.7 0.8 0.9 1

He

at T

rnas

fer

Co

eff

icie

nt,

W/m

2K

Vapor Quality

Measured

w/El Hajal Map

w/Baker Map

Fig. 1 Predictions of the present correlation using the flow pattern maps of El Hajal et al. and Baker. Data of

Varma [10] for water. TSAT = 82 oC, pr = 0.0023, = 12.6 kg/m

2s.

4. NEW FLOW PATTERN BASED CORRELATION

Based on the results of the above described data analysis, the following flow pattern based correlation is

proposed:

If flow pattern is intermittent, annular, or mist:

ITP hh (11)

If flow pattern is stratified-wavy:

NuITP hhh (12)

If flow pattern is stratified:

NuTP hh (13)

To determine flow patterns, it is recommended to use the Baker map for low pressure water and the El Hajal et al. map for other fluids. Applicability of other flow pattern maps is unknown.

5. COMPARISON WITH TEST DATA

5.1 Data Search and Collection

A wide ranging database was available from the author’s earlier researches, Shah [2, 3]. Recent literature was

searched to obtain data for wider range of parameters and for fluids not included in that database. This resulted

in procurement of data for butane, R-236ea, R-1234yf, and R-1234ze. The new database thus contains 25 fluids. The complete range of data analyzed is listed in Tables 1 and 2. Data for different fluids or of different diameters

were considered separate data sets even if they are from the same source. For refrigerants, only oil-free data was

considered as oil can have profound effect on heat transfer. Further, data for mixtures with glide more than 1

degree C were not included as heat transfer of mixtures with large glide is reduced due to mass transfer effects.

IHTC15-8645

5

Table 1 Complete range of parameters in the data analyzed.

Fluids Water, R-11, R-12, R-22, R-32, R-113, R-123, R-125,

R-134a, R-142b,R-236ea, R-404A, R-410A, R-502, R-

507, R1234ze, R-1234yf, benzene, butane, isobutane,

propylene, propane, benzene, DME, CO2

Tube dia., mm 2 to 49

Reduced pressure 0.002 to 0.946

, kg/m2s 13 to 820

ReLT 1012 to 84827

ReGT 15892 to 599510

x 0.01 to 0.99

Number of data points 1528

Number of data sources 38

Number of data sets 88

Data for tubes of diameters smaller than 2 mm were excluded from consideration as these are generally regarded

as mini/micro channels and their heat transfer behavior is considered to be different from that of larger tubes.

5.2 Correlations Tested

To put the performance of the new correlation into perspective, it is desirable that other leading correlations be

also tested along with it. Only a few correlations are available which have been verified with data covering the entire range from very low flow rates to very high flow rates. Perhaps the most verified among these is that of

Cavallini et al. [14]. This correlation has two heat transfer regimes called the heat flux independent and the heat

flux dependent regimes and there are different formulas for the two regimes. To analyze the data in the heat flux

dependent regime with this correlation, heat flux must be known. Most of the data sets analyzed do not report heat flux. Hence only the data in their heat flux independent regime can be compared to the Cavallini et al.

correlation. Similar is the situation with the other correlations which have been demonstrated applicable to

extreme range of data such as that of Dobson and Chato [15] and Thome et al. [9].

Many other correlations have been proposed which have had considerable verification and their authors have not

given any limits for their applicability. Among such correlations are those Akers et al. [16], Ananiev et al. [17],

and Moser et al. [18]. These correlations and the correlation of Shah [2, 3] and the new flow pattern based correlation were compared to the entire database.

5.3 Calculation Method

The entire database was compared to all correlations except the Cavallini et al. correlation which was compared only to those data which were in its heat flux independent regime. A run was also made in which all correlations

were compared only with those data which were in heat flux independent regime of Cavallini et al. Flow patterns

were determined using the Baker map for water and the El Hajal et al. map for all other fluids. Fluid properties were calculated with REFPROP 9.1 [19]. Single phase heat transfer coefficient for the present and Shah

correlations was calculated by Eq. (6) for all data except those of Son & Lee [20] for which the following

equation was used:

Dkh llLSLS /PrRe034.0 3.08.0 (14)

The reason is that these authors’ single-phase measurements were higher than Eq. (6) and they fitted Eq. (14) to

their data.

The results of calculations are given in Tables 2 and 3.

IHTC15-8645

6

Table 2 Salient features of data for horizontal tubes and results of comparison with the Shah Correlation [3] and present correlation using flow patterns as criteria.

Source Dia.,

mm

Fluid pr

Kg/m2s

x ReLT ReGT No.

of

Data

Deviation, Percent

Mean Absolute

Average

Shah [3] Present

Wilson et al.

[26]

3.72** R-410A 0.435 75

400

0.80

0.10

2698

14390

19322

103052

12 10.7

7.8

13.7

10.7

R-134a 0.218 75

400

0.79

0.10

1619

8635

23010

122718

13 14.7

-0.1

17.0

2.2

Zilly [27] 6.1 CO2 0.227

0.309

200

400

0.80

0.10

8046

18973

95529

191058

16 28.7

28.7

28.7

28.7

R-22 0.049 400 0.78

0.20

9031

12575

206932

231699

7 15.1

15.1

15.1

15.1

Shao et al.

[28]

9.4 R-134a 0.249 100

400

0.80

0.10

5811

23245

76018

304071

20 6.4

-3.0

9.5

-2.8

Iqbal &

Bansal [29]

6.52 CO2 0.309

0.470

50

200

0.98

0.02

2535

13085

24216

96862

83 27.6

5.1

24.2

-5.7

Kondou & Hrnjak [30]

6.1 CO2 0.810 0.946

100 200

0.98 0.10

9687 19374

32472 64945

31 13.5 -9.1

13.6 -12.1

Afroz &

Miyara [25]

4.35 DME 0.127 200

500

0.97

0.02

7081

17703

91698

229244

29 12.5

-11.4

11.8

-10.5

Wen, Ho, &

Hsieh [31]

2.46 Butane

(R-600)

0.099 205

510

0.84

0.12

3661

9107

64805

161202

18 15.1

-14.4

15.1

-14.4

R-134a 0.249 205

510

0.84

0.12

3118

7556

40783

101459

18 9.9

2.6

11.9

4.6

Propane 0.321 205

510

0.80

0.13

6077

15119

56760

141207

18 10.8

-8.5

10.8

-8.5

Dalkilic & Agra [32]

4.0 Isobutane 0.127 57 92

0.90 0.05

1671 2698

29362 47392

17 7.9 -6.3

17.9 17.9

Son & Lee

[33]

5.35 R-134a 0.249 400 0.88

0.08

13230 173062 5 12.0

11.9

12.0

11.9

R-22 0.306 300 0.88

0.12

11554 120231 6 4.0

0.8

4.3

3.4

3.36 R-134a 0.249 200

400

0.90

0.10

4154

8309

54345

108689

15 8.4

-5.3

9.3

-1.0

R-22 0.306 200

400

0.88

0.09

7256

9675

75510

100679

12 9.6

-1.2

9.6

-1.2

Lee & Son

[34]

5.8 Propane 0.321 49

170

0.85

0.05

3443

11882

32248

110976

13 19.3

-19.3

24.4

-24.3

6.54 Propane 0.321 56

133

0.85

0.06

4445

10482

41515

97900

12 9.1

1.2

13.9

-1.2

7.73 Propane 0.321 62

100

0.83

0.05

5813

9336

54289

87002

12 16.4

1.4

24.5

7.3

10.07 Propane 0.321 47 0.80

0.05

5704

53270 9 20.1

20.1

28.5

6.7

5.8 Isobutane 0.146 49

170

085

0.05

2211

7609

36231

124681

13 25.0

-25.0

22.2

-20.3

6.54 Iso-butane 0.146 52

152

0.85

0.05

2609

7671

42756

125703

12 17.4

-17.4

9.8

-8.7

7.73 Iso-butane 0.146 51 0.86

0.06

3054 50046 10 16.7

3.7

16.8

6.6

10.07 Isobutane 0.146 49

115

0.87

0.05

3889

8936

62904

146437

12 12.0

10.0

19.7

1.5

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7

5.8 R-134a 0.146 42 0.86

0.06

1510 19747 10 42.0

-42.0

42.0

-42.0

6.54 R-134a 0.249 74

160

0.85

0.05

2106

6449

39138

84622

12 15.7

12.2

28.0

-0.3

7.73 R-134a 0.249 52

165

0.80

0.05

2509

7885

32819

103146

11 29.0

16.6

26.3

11.7

10.07 R-134a 0.249 52

112

0.84

0.05

3268

6972

42754

91281

10 20.7

-8.6

38.8

35.2

5.8 R-22 0.306 50

152

0.85

0.06

2100

6346

21854

66041

11 14.6

12.9

26.6

-0.8

6.54 R-22 0.306 56

210

0.85

0.06

2636

9886

27435

102882

12 42.8

42.7

34.5

28.6

7.73 R-22 0.306 52

190

0.89

0.05

2921

10572

30400

110021

12 14.8

-14.8

31.9

14.2

10.07 R-22 0.306 50

150

0.85

0.06

3632

10872

37793

113152

11 19.1

7.1

37.8

37.0

Hossain et

al.[35]

0.306 R-32 0.427 300 0.90

0.08

13713 94445 7 24.6

-24.6

24.6

-24.6

0.306 R-1234ze 0.210 191

375

0.96

0.10

4966

9750

64295

126233

29 27.0

-27.0

24.4

-24.4

Varma [10] 49.0 water 0.002 12.6 0.95

0.58

1808 54415 4 31.1

-24.6

6.2

0.9

Tang et al.

[36]

8.8 R-134a 0.25 260

820

0.81

0.09

11573

36500

181808

573395

24 12.2

7.4

13.3

9.7

R-410A 0.495 320

720

0.81

0.09

29822

73624

191929

473824

16 11.6

8.8

11.6

8.8

R-22 0.308 270

790

0.91

0.09

11591

33914

165849

485263

28 5.7

-0.4

5.3

0.1

Bae et al. [37] 12.5 R-22 0.235

0.325

210

634

0.90

0.09

12579

38430

193612

569436

27 16.4

4.0

16.0

4.4

Bae et al. [38] R-12 0.197

0.211

344

634

0.91

0.03

17721

32932

327303

599510

29 14.2

-7.9

13.8

-7.5

Powell [39] 12.8 R-11 0.035 258 0.24 8689 283628 1 2.0

2.0

2.0

2.0

Lambrecht et

al. [40]

8.1 R-22 0.308 300

800

0.5 11854

31611

169619

452317

6 31.1

31.1

31.1

31.1

Jung et al.

[41]

8.0 R-32 0.428 100

300

8430

25290

55402

166205

17 13.2

1.1

12.6

2.2

R-12 0.127 100

300

0.93

0.10

4253

12759

63431

190294

14 12.3

1.2

12.1

2.4

R-125 0.559 100

300

0.90

0.15

7306

21918

42781

128342

13 8.3

-8.3

8.3

-8.3

R-123 0.042 100

300

0.90

0.15

2675

8024

70573

211720

15 12.1

6.4

15.1

12.3

R-142b 0.128 100

300

0.92

0.2

4073

12220

72727

218182

17 9.4

-1.4

9.7

6.7

Infante-Ferreira et al.

[42]

8.0 R-404A 0.491 250 600

0.88 0.14

19605 47053

150036 360086

16 13.5 -10.3

13.5 -10.3

Park et al.

[43]

8.8 Propy-

lene

0.354 100

300

0.91

0.10

10784

32355

90072

270215

28 32.5

32.5

37.9

37.9

Isobutane 0.146 100

300

0.89

0.10

6882

20646

110913

332739

21 10.8

9.6

16.4

15.9

Propane 0.322 100

300

0.88

0.1

10643

31930

93739

281217

27 18.8

18.8

22.2

22.2

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8

R-22 0.308 100

300

0.90

0.10

4293

12879

61426

184277

27 7.6

1.6

10.8

2.1

Jiang &

Garimella

[44]

9.4 R-404A 0.805

0.907

200

500

0.88

0.20

28415

84827

96507

275264

40 8.7

-4.1

9.2

-4.5

Lee et al. [45] 10.9 Propylene 0.354 150 0.88

0.01

20074

167656 10 17.2

-17.2

15.3

-14.1

Isobutane 0.146 150 0.88

0.01

12810 206450 10 14.1

-14.1

11.6

-11.6

Propane 0.32 150 0.90

0.01

19811

174483 10 13.5

-13.5

12.5

-12.1

R-22 0.308 150 0.91

0.01

7991 114336 10 18.0

-18.0

22.6

-22.6

Jung et al.

[46]

8.8 R-134a 0.250 100

300

0.98

0.05

4461

13384

70085

210255

27 10.6

-7.7

9.2

-4.5

R-410A 0.495 100 300

0.94 0.03

9341 28022

60114 180342

27 9.3 -9.3

8.1 -6.0

R-22 0.308 100

300

0.96

0.08

4303

12908

61565

184696

26 15.5

-12.7

13.6

-8.7

Eckels &

Tesene [47]

8.0 R-507 0.505 251

599

0.80

0.10

19844

47455

147434

352565

23 14.3

5.4

15.2

6.3

R-502 0.411 600 0.75

0.13

38989 342547 8 21.4

21.4

21.4

21.4

Eckels et al.

[48]

8.0 R-12 0.233 134

374

0.47*

0.43

4560

12726

79488

221742

5 12.8

12.1

16.1

16.1

8.0

R-134a 0.245 87

368

0.50*

3511

14851

55531

234889

7 8.6

8.5

8.6

8.5

11.0 R-134a 0.249 84

280

0.51*

0.47

5712

19041

74724

249080

5 4.

1.5

7.6

5.3

Nan &

Infante-

Fereira [49]

8.8 Propane 0.286 150

250

0.59

0.10

15132

25220

144510

240849

6 9.6

-8.1

11.9

-4.8

Dobson &

Chato [15]

7.0 R-410A 0.438 75

650

0.90

0.09

5172

44827

37258

322900

18 11.7

-10.2

13.0

-11.5

R-22 0.272 75

650

0.90

0.16

2558

22171

37768

327323

18 11.0

-8.5

13.2

-10.6

R-134a 0.219 75 650

0.9 0.09

2622 22725

42961 372331

19 12.5 -11.5

12.5 -11.5

Wijaya &

Spatz [50]

7.7 R-22 0.272

0.405

481

495

0.80

0.21

18138

18587

245041

274408

18 7.7

-4.6

7.7

-4.6

R-410A 0.573

0.652

481 0.79

0.25

43405

47297

231147

242447

13 14.0

-14.0

14.0

-14.0

Shao &

Granyrd [51]

6.0 R-134a 0.189

0.191

183

269

0.92

0.10

6030

8797

92064

135629

10 15.3

10.1

20.4

17.8

Cavallini et

al. [52]

8.0 R-134a 0.250 65

750

0.80

0.28

2630

30349

41320

476769

37 8.3

-2.0

9.3

-2.0

R-410A 0.495 750 0.75

0.20

63542 408939 7 20.9

20.9

20.9

20.9

R-125 0.559 100

750

0.80

0.23

7306

54795

42781

320856

23 10.7

0.2

10.6

1.1

R-32 0.429 100

600

0.80

0.24

8430

50580

55402

332410

24 11.1

6.8

10.4

8.6

R-22 0.308 100

750

0.85

0.20

3903

29270

55842

418812

31 9.8

-3.4

8.7

-2.2

R236ea 0.098 100

650

0.840

.20

2554

15323

70555

423333

28 12.3

-12.1

5.4

-4.2

IHTC15-8645

9

Altman et al.

[53]

8.7 R-22 0.268

0.441

300

618

0.92

0.23

12725

26166

184687

379779

15 8.4

-7.4

6.4

-5.3

Azer et al.

[54]

12.7 R-12 0.219

0.296

210

446

0.99

0.35

115362

4690

195269

411239

39 29.2

22.3

31.4

26.7

Chitti &

Anand [55]

8.0 R-22 0.272

0.356

149

437

0.75

0.20

5793

17124

84608

236958

12 13.4

-12.2

10.3

-9.1

Berrada et al.

[56]

8.9 R-134a 0.278 170

214

0.79

0.25

7765

9774

117866

148373

14 23.7

23.7

32.4

32.4

R-22 0.312 114

214

0.80

0.12

4963

9317

70769

132846

12 11.9

5.8

14.9

9.2

Jassim et al.

[57]

8.9 R-134a 0.164 100

300

0.94

0.04

75125

12663

75125

225375

25 20.0

-20.0

18.0

-18.0

Akers et al.

[16]

15.7 R-12 0.662 78

418

0.94*

0.63

6786

36356

67301

360575

33 24.4

20.9

20.4

20.4

Propane 0.657 13 162

0.83*

0.51 3899

48103 17473

215578 15 16.9

6.9 18.2 12.8

Tepe &

Mueller [58]

18.5 Benzene 0.021 54

82

0.57*

0.51

3264

4991

106965

163546

6 10.2

-2.8

5.7

5.7

Yan and Lin

[59]

2.0 R-134a 0.16

0.32

100

200.

0.94

0.10

1012

2076

15892

33764

31 14.3

-3.2

19.3

19.0

Wang et al.

[60]

4.0 R-1234yf 0.12

0.92

101

401

0.300

0.384

3163

14023

32141

13916

40 31.3

-31.3

21.5

-21.4

All data 2.0

49.0

0.002

0.946

13

820

0.98

0.01

1012

84827

15892

599510

1568 16.1

-0.9

16.7

1.2

*Mean quality for the tube length **Hydraulic equivalent diameter of flattened tube

Table 3 Results of data analysis for all tested correlations

Correlation Deviation, Percent

Mean Absolute

Average

Heat Flux

Independent Regime*

(675 data points)

All Data

(1568 data points)

Ananiev et al. [17] 19.5

-16.2

27.0

-24.8

Moser et al. [18] 19.4

8.9

22.8

3.4

Cavallini et al. [14] 15.0

-8.5

Not applied to heat flux

dependent regime data

Akers et al. [16] 37.8 -37.6

43.3 -43.2

Shah [3] 14.1

0.4

16.1

-0.9

Present 14.2 2.4

16.7 1.2

*Regime according to Cavallini et al. (2006) correlation.

Mean absolute deviation is defined as:

N

measuredmeasuredpredictedm hhhABSN 1

/)(1

(15)

IHTC15-8645

10

Average deviation is defined as:

N

measuredmeasuredpredictedavg hhhN 1

/)(1

(16)

6. DISCUSSION OF RESULTS

Detailed results of data analysis for the present correlation and the Shah [3] correlation are listed in Table 2. The

present correlation has a mean absolute deviation of 16.7 % while the Shah correlation has a mean absolute

deviation of 16.1 %. Of the 89 data sets analyzed, 21 show better agreement with the present correlation while 25 show better agreement with the Shah correlation, the mean deviations of the remaining 43 being unchanged.

If more data sets are analyzed, the balance may well change. Thus the accuracy of the present flow pattern based

correlation is perhaps a little less than that of the Shah correlation which uses heat transfer regimes without any physical meaning. This small loss of accuracy may be acceptable in exchange for the physical clarity.

Table 3 lists the results for all correlations and Figs. 2 to 6 show some of the results in graphical form. Considering all data, it is seen that all correlations have considerably larger deviations than the present and the

Shah correlations. The next best is the correlation of Moser et al. with 22.8 % deviation. Considering only those

data which are in the heat flux independent regime of Cavallini et al. [14] correlation, the deviations of the

present and the Shah correlation are almost equal at 14.2 and 14.1 % respectively. The performance of the Cavallini et al. correlation is also good with a mean deviation of 15.0 %. Notably poor is the performance of the

Akers et al. [16] correlation with a mean deviation of 43.3 % and average deviation of -43.2 %. The other

correlations give fairly good performance. Figs. 2 to 6 show comparison of data with the present and other correlations.

As seen in Table 2, agreement of the present correlation with near azeotropic mixtures R-410A and R-404A is

good. Heat transfer of fluids with large glides is considerably diminished due to effects of sensible heat transfer and mass transfer as the mixture composition and the temperature of components changes along the tube. Shah

et al. [21] analyzed an extensive database of mixtures with glides upto 35 OC. They found that the Shah [2]

correlation gave good agreement when used with the correction factors given by Bell and Ghaly [22] and McNaught [23]. Good agreement is also expected with the present correlation in the same way as the El Hajal et

al. map was also verified with data for mixtures.

Data for tubes with diameters smaller than 2 mm were not included in the present data analysis. Shah [24] had

compared a large database for mini-channels with his correlation [2] and found that many of those data sets were

in good agreement while others showed large deviations. That correlation does not consider flow patterns. It will

be interesting to compare those data with the present correlation using flow pattern maps applicable to mini-channels. It will also be interesting to compare this correlation to data for non-circular channels using flow

pattern maps applicable to them.

In evaluating the results of this data analysis, knowing the accuracy of the test data could be helpful in

understanding the deviations from the correlation. Most authors have given only the accuracy of the test

instruments used and it is always 2 % or better. A few have done the error propagation analysis to determine the uncertainty in heat transfer coefficients; the reported uncertainties are in the range of 2.3 to 9.5 percent except

that Lambrecht et al. [40] estimate it as upto 14.7 %; their data show mean deviation of 31 % which suggests that

it may be due to data inaccuracy. Some researchers tested several fluids on the same test rig, for example Park et

al. [43]. The deviations of their data for two fluids are low but are high for propylene. Data of Lee et al. [45] for propylene at comparable conditions show good agreement. Thus researchers’ own estimates of uncertainty of

data are not always helpful. Using data from many sources is probably the best way to identify doubtful data.

The correlation is recommended in the verified range of pr. Therefore for water it is recommended only at pr near

0.002 as the data analyzed are only at this pressure and because properties of water differ significantly from

other fluids. For other fluids, the verified range of pr is 0.02 to 0.95. Further, it is recommended only in the

verified range of ReLT (1,012 to 84,827) and ReGT (15,892 to 599,510).

IHTC15-8645

11

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 0.2 0.4 0.6 0.8 1

He

at T

ran

sfe

r C

oe

ff.,

W/m

2K

Quality

Measured

Present

Ananiev

Moser

Akers

R-236ea

Fig. 2 Comparison of test data of Cavallini et al. [52] with various correlations. TSAT = 40 oC, = 600

kg/m2s.

0

1000

2000

3000

4000

5000

6000

0 0.2 0.4 0.6 0.8 1

He

at T

ran

sfe

r C

oe

ffic

ien

t, W

/m2K

Vapor Quality

Measured

Shah

Present

Moser

Akers

Fig. 3 Comparison of the data of Jung et al. [41] for R-142b with various correlations. TSAT = 40 oC, =

300 kg/m2s.

0

500

1000

1500

2000

2500

3000

3500

0 0.2 0.4 0.6 0.8 1

He

at T

ran

sfe

r C

oe

ffic

ien

t, W

/m2K

Vapor Quality

Measured

Present

Ananiev

Moser

Akers

Fig. 4 Comparison of various correlations with the data of Kondou & Hrnjak [30] for CO2, = 100 kg/m2s,

pr = 0.81.

IHTC15-8645

12

0

500

1000

1500

2000

2500

3000

3500

0 0.2 0.4 0.6 0.8 1

He

at T

ran

sfe

r C

oe

ffic

ien

t, W

/m2K

Vapor Quality

Measured

Present

Ananiev

Moser

Akers

Fig. 5 Comparison of various correlations with the data of Lee & Son [34] for propane. D = 6.54 mm, TSAT

= 40 oC, = 56 kg/m

2s.

1000

1500

2000

2500

3000

3500

4000

4500

0 0.2 0.4 0.6 0.8 1

He

at T

ran

sfe

r C

oe

ffic

ien

t, W

/m2K

Vapor Quality

Meaured

Present

Ananiev

Moser

Fig. 6 Comparison of various correlations with the data of Shao et al. [28] for R-134a. = 300 kg/m2s. TSAT

= 40 oC.

7. CONCLUSION

1. A flow pattern based correlation for heat transfer during condensation inside plain tubes has been

presented which shows good agreement with data for 25 fluids over an extreme range of parameters

including tube diameters from 2 to 49 mm, reduced pressures from 0.002 to 0.94, and mass flow rates

from 13 to 820 kg/m2s.

2. A number of other general correlations were also compared to the same data base. The accuracy of the

new flow pattern based is slightly lower than that of the Shah [3] correlation but it is more clearly

related to the physical phenomena involved. Its accuracy compares favorably with other correlations.

IHTC15-8645

13

3. For water, there were only a few data points at low pressure and all from one source. While use of the

Baker map resulted in good agreement with data, analysis of water data at higher pressures and more

varied conditions is needed.

4. Based on the results of data analysis in Table 2, the present correlation is recommended for pure fluids

other than water in the following range: pr = 0.02 to 0.095, ReLT = 1,012 to 84,827 , ReGT = 15,800 to

599,510 . For water, application should be further restricted to pr near 0.002 till verification with higher

and lower pressure data is done.

5. The present correlation is likely to be applicable to mixtures when used with the correction factors of

Bell and Ghaly [22] and McNaught [23].

NOMENCLATURE

D Inside diameter of tube (m) Total mass flux (liquid + vapor) (kg/m

2s)

g Acceleration due to gravity (m/s2)

h Heat transfer coefficient (W/m2K)

hI Heat transfer coefficient given by Eq. (1) (W/m2K)

hLS Heat transfer coefficient assuming liquid phase flowing alone in the tube (W/m2K)

hLT Heat transfer coefficient assuming all mass flowing as liquid (W/m2K)

hNu Heat transfer coefficient given by Eq. (2), the Nusselt relation (W/m2K)

hTP Two-phase heat transfer coefficient (W/m2K)

Jg Dimensionless vapor velocity defined by Eq. (10) (-)

N Number of data points (-) pr Reduced pressure (-)

ReGT Reynolds number assuming total mass flowing as vapor, = D/μg (-)

ReLS Reynolds number assuming liquid phase flowing alone, = (1-x)D/μl (-)

ReLT Reynolds number assuming total mass flowing as liquid, = D/μl (-) TSAT Saturation temperature (C)

x Vapor quality (-)

Z Shah’s correlating parameter, defined by Eq. (7) (-)

REFERENCES

[1] Shah, M.M. ,” A general correlation for heat transfer during film condensation in pipes,” Int. J. Heat Mass Transfer, 22, pp.

547-556, (1979).

[2] Shah, M. M.,” An improved and extended general correlation for heat transfer during condensation in plain tubes,” HVAC&R

Research,” 15(5), pp. 889-913, (2009).

[3] Shah, M. M. ,” General correlation for heat transfer during condensation in plain tubes: further development and verification,”

ASHRAE Trans. 119(2), pp. 3-11, (2013).

[4] Liebenberg, L. and Meyer, J. P. ,” A review of flow pattern based predictive correlations during refrigerant condensation in

horizontally smooth and enhanced tubes,” Heat Transfer Engineering,” 29(1):3-18, (2008).

[5] McAdams, W. H., Heat Transmission, New York: McGraw Hill, (1954).

[6] Breber, G., Palen, J. W., J. Taborek, J. ,” Prediction of horizontal tubeside condensation of pure components using flow regime

criteria,” J. Heat Transfer, 102(3), pp. 471-476, (1980).

[7] Tandon, T. N., Varma, H. K., Gupta, C. P., “A new flow regime map for condensation inside horizontal tubes,” J. Heat

Transfer, 104(4), pp. 763-768, (1982).

[8] El Hajal, J., Thome, J. R., Cavallini, A. ,” Condensation in horizontal tubes, part I: two-phase flow pattern map,” Int. J. Heat

Mass Trans. 46, pp. 3349-3363, (2003).

IHTC15-8645

14

[9] Thome, J. R., J. El Hajal, A. Cavallini, “Condensation in horizontal tubes, part 2: new heat transfer model based on flow regimes,” Int. J. Heat Mass Transfer, 46, pp. 3365-3387, (2003).

[10] Varma, V. C. , A study of condensation of steam inside a tube. Master of Science Thesis, Rutgers University, NJ, (1977). [11] Baker, O., “Design of pipelines for flow of oil and gas,” Oil Gas J., 53, pp.185-195, (1954). [12] Shah, M. M., “Visual observations in an ammonia evaporator,” ASHRAE Trans., 82(1), (1975).

[13] Taitel, Y. and Dukler, A. E., “A model for predicting flow regime transitions in horizontal and near-horizontal gas-liquid flow,” AIChE J., 22(1), pp. 47-55, (1976).

[14] Cavallini, A., Col, D. D., .Doretti, L., Matkovic, M., Rossetto, L., Zilio, C., “Condensation in horizontal smooth tubes : a new heat transfer model for heat exchanger design,” Heat Transfer Engineering, 27(8), pp. 31-38, (2006).

[15] Dobson, M. K. and J. C. Chato, “ Condensation in smooth horizontal tubes,” J. Heat Transfer, 120, pp. 193-213, (1998). [16] Akers, W. W., Deans, H. A., and Crosser, O. K. “Condensing heat transfer within horizontal tubes,” Chem. Eng. Prog. Symp.

Ser., 59(29), pp. 171- 176, (1959). [17] Ananiev, E. P., Boyko, I. D., and Kruzhilin, G. N. , “Heat Transfer in the Presence of Steam Condensation In Horizontal

Tubes,” in S Yagi, D Kunii, and N Wakoo, eds. Int. Developments in Heat Transfer, part 2, New York, ASME, pp. 290-295, (1961).

[18] Moser, K. W., Webb, R. L., Na, B., “ A new equivalent Reynolds number model for condensation in smooth tubes,” J. Heat Transfer,” 120, pp. 410-416, (1998).

[19] Lemmon, E. W., Huber, M. L., and McLinden, M. O., NIST Reference Fluid Thermodynamic and Transport Properties, REFPROP Version 9.1, NIST, Gaithersburg, MD. (2013)

[20] Son, C. and Lee, H., “Condensation heat transfer characteristics of R-22, R-134a and R-410A in small diameter tubes,” Heat Mass Transfer, 45, pp. 1153-1166, (2009).

[21] Shah, M. M. , Mahmoud, A. M., and Lee, J., “An assessment of some predictive methods for in-tube condensation heat transfer of refrigerant mixtures,” ASHRAE Trans.,119(2), pp. 38-51, (2013).

[22] Bell, K.J., and Ghaly. M. A., “An approximate generalized method for multicomponent partial condenser,” American Institute of Chemical Engineers Symposium Series ,69, pp. 72–79, (1973).

[23] McNaught, J. M., “Mass-Transfer Correction Term in Design Methods for Multicomponent/Partial Condensers,” in eds. P. J.Marto and and P. G. Kroeger, Condensation Heat Transfer, New York, ASME, pp. 111-118, (1979).

[24] Shah, M. M., “Heat Transfer During Condensation Inside Small Channels: Applicability of General Correlation for Macrochannels,” Proc. of 14th International Heat Transfer Conference, IHTC14-22346, (2010)

[25] Afroz, H.M M., Miyara, A. and K. Tsubaki,, “Heat transfer coefficients and pressure drops during in-tube condensation of CO2/DME mixture refrigerant,” Int. J. Refrigeration, 31, pp. 1458-1466, (2008).

[26] Wilson, M. J., Newell, T. A., Chato,J. C., and Infante Ferreira, C. A., “ Refrigerant charge, pressure drop, and condensation heat transfer in flattened tubes,” Int.J.Refrig., 26, pp. 443-451, (2003).

[27] Zilly, J., Jang, J, Hrnjak, P., “ Condensation of CO2 at low temperature inside horizontal micro-finned tube,” ACRC Report CR-49, University of Illinois at Urbana Champaign , (2003)

[28] Shao, L., Han, J., Su, G., and Pan, J., “Condensation heat transfer of R-134A in horizontal straight and helically coiled tube-in-tube heat exchangers,” Journal of Hydrodynamics, Ser. B, , pp. 677-682, (2007).

[29] Iqbal, O., and Bansal, P. “In-tube condensation of CO2 heat transfer in a horizontal smooth tube,” International J. Refrig.,

35(2), pp. 270-277, (2012). [30] Kondou, C., and Hrnjak, P., ”Heat rejection from R744 flow under uniform temperature cooling in a horizontal smooth tube

around the critical point,” Int. J. Refrig., 34, pp. 719-731, (2011). [31] Wen, M., Ho, C., and Hsieh, J. ,” Condensation heat Transfer and pressure drop characteristics of R-290 (propane), R-600

(butane), and a mixture of R-290/R-600 in the serpentine small-tube bank,” Applied Thermal Engineering, 26, pp. 2045-2053, (2006).

[32] Dalkilic, A. S., and Agra, O., “Experimental Apparatus for the Determination of Condensation Heat Transfer Coefficients for

R-134a and R-600a Flowing Inside Vertical and Horizontal Tubes Respectively,” Proc. of the 2009 ASME Summer Heat

Transfer Conference, San Francisco, California, USA, (2009).

[33] Son, C. and Lee, H., “Condensation characteristics of R-22, R-134a, and R-410A in small diameter tubes,” Heat & Mass Transfer, 45, pp. 1153-1166, (2009).

[34] Lee, H., and Son, C., “Condensation heat transfer and pressure drop characteristics of R-290, R-600a, R-134a, and R-22 in horizontal tubes,” Heat Mass Transfer, 46, pp. 571-584, (2010).

[35] Hossain, M. A., Onaka, Y., and Miyara, A., “Experimental study on condensation heat transfer and pressure drop in horizontal plain tubes for R-1234ze(E), R-32, and R-410A,” Int. J. Refrigeration, 35, pp. 927-938, (2012).

[36] Tang, L., Ohadi, M. M. and Johnson, A. T., “ Flow condensation in smooth and micro-fin tubes with HCFC-22, HFC-134a and HFC-410A refrigerants,” Enhanced Heat Transfer, 7, pp. 289-310, (2000).

[37] Bae, J., Maulbetsch, L., and Rohsenow, W. M., “Refrigerant forced convection condensation inside horizontal tubes,” M.I.T Report DSR-79760-64, (1969).

[38] Bae, J., Maulbetsch, L., and Rohsenow, W. M., “Refrigerant forced convection condensation inside horizontal tubes,” M.I.T Report DSR-79760-59, (1968).

[39] Powell,C.K. , Condensation Inside a Horizontal Tube with High Vapor Velocity. M.S. Thesis, Purdue University, (1961). [40] Lambrecht, A., Liebenberg, L., Bergles, A. E., and Meyer, J. P. , “ Heat transfer performance during condensation inside

horizontal smooth, micro-fin, and herringbone tubes,” J. Heat Transfer, 128(7), pp. 691-700, (2006). [41] Jung, D., Song, K., Cho, Y., and Kim, S., “Flow condensation of heat transfer coefficients of pure refrigerants,” Int. J.

Refrigeration, 26, pp. 4-11, (2003).

IHTC15-8645

15

[42] Infante-Ferreira, C. A., Newell, T. A., Chato,J. C., and X. Nan, X., “ R404A condensing under forced flow conditions inside smooth, microfin and cross-hatched tubes,” Int. J. Refrigeration, 26, pp. 433-441, (2002).

[43] Park, K., Jung, D. and Seo, T., “Flow condensation heat transfer characteristics of hydrocarbon refrigerants and dimethyl ether inside a horizontal plain tube,” Int. J. Multiphase Flow, 4, pp. 628-635, (2008).

[44] Jiang, Y., and Garimella, S., “Heat transfer and pressure drop for condensation of R-404A at near critical pressure,” ASHRAE

Trans., 109(1), pp. 677-688, (2003). [45] Lee, H., Yoon, J., Kim, J., and Bansal, P. K., “Condensing heat transfer and pressure drop characteristics of hydrocarbon

refrigerants,” Int. J. Heat Mass Transfer, 49, pp. 1922-1927, (2006). [46] Jung, D., Cho, Y., and Park, K., “Flow condensation heat transfer coefficients of R22, R134a, R407C, and R410A inside plain

and microfin tubes,” Int. J. Refrigeration, 27, pp. 25-32, (2004). [47] Eckels, S. J. and Tesene, B., “Forced convective condensation of refrigerants R-502 and R-507 in smooth and enhanced

tubes,” ASHRAE Trans., 99, pp. 627-638, (1993). [48] Eckels, S, Doerr, T. M., and Pate, M. B., “Heat transfer and pressure drop during condensation and evaporation of R-134a/oil

mixtures in smooth and micro-fin tubes.” Final Report ASHRAE RP-630, (1993). [49] Nan, X. H. and Infante Ferreira, C. A., “In-Tube Evaporation and Condensation of Natural Refrigerant R 290 (Propane),”

Preliminary Proceedings of the 4th IIR Gustav Lorentzen Conference on Natural Working Fluids,IIR Commission B1, B2, E1, E2, Purdue, (2000).

[50] Wijaya, H. and Spatz, M. W., “Two-phase flow heat transfer and pressure drop characteristics of R-22 and R-32/R125,” ASHRAE Trans., 101(1), pp. 1020-1027, (1995).

[51] Shao, D. W. and Granryd, E., “Heat transfer and pressure drop of HFC134a-oil mixtures in horizontal condensing tube,” Int. J. Refrig., 18(8), pp. 524-533, (1995).

[52] Cavallini, A., Censi, G., Col, D. D., Doretti, L., Longo, G. A., and Rossetto, L., “ Experimental investigation on condensation heat transfer and pressure drop of new HFC refrigerants (R134a, R125, R32, R410A, R236ea) in a horizontal smooth tube,” Int. J. Refrig., 21, pp. 73-87, (2001).

[53] Altman, M., Staub, F. W., and Norris, R. H., “Local heat transfer and pressure drop for Refrigerant 22 condensing in horizontal tubes,” ASME-AIChE Conf., Storrs, CT., (1979).

[54] Azer, N. Z., Abis, L. V., and Soliman, H. M., “Local heat transfer coefficients during annular flow condensation,” ASHRAE Trans., 78, pp. 135-143, (1972).

[55] Chitti, M.S. and Anand, N. K., “An analytical model for local heat transfer coefficients for forced convective condensation

inside smooth horizontal tubes,” Int. J. Heat Mass Transfer, 2, pp. 615-627, (1995). [56] Berrada, N., Marviller, C., Bontemps, A., and Daudi., S. , “Heat transfer in tube condensation of a zeotropic mixture of

R23/134a in a horizontal smooth tube,” Int. J. Refrig., 19(7), pp. 463–72, (1996). [57] Jassim, E. W., Newell, T. A., Chato, J. C., “Prediction of two-phase condensation in horizontal tubes using probabilistic flow

regime maps,” Int. J. Heat Mass Transfer, 51(3-4), pp. 485-496, (2008) [58] Tepe, J.B. and Mueller, A.C., “Condensation and subcooling inside an inclined tube,” Chem. Eng. Prog., 43, pp. 267-278,

(1947). [59] Yan, Y. and Lin, T., “Condensation heat transfer and pressure drop of refrigerant R-134a in a small pipe,” Int. J. Heat Mass

Transfer, 42, pp. 697-708, (1999).

[60] Wang, L., Dang, C., and Hihara, E.,”Experimental study on condensation heat transfer and pressure drop of low GWP refrigerant HFO 1234yf in a horizontal tube,” Int. J. Refrig., 35(5), pp. 1418-1429, (2013).